This equation will change how you see the world (the logistic map)

The logistic map connects fluid convection, neuron firing, the Mandelbrot set and so much more. Fasthosts Techie Test competition is now closed! Learn more about Fasthosts here: Code for interactives is available below...
Animations, coding, interactives in this video by Jonny Hyman 🙌
Try the code yourself:
James Gleick, Chaos
Steven Strogatz, Nonlinear Dynamics and Chaos
May, R. Simple mathematical models with very complicated dynamics. Nature 261, 459-467 (1976).
Robert Shaw, The Dripping Faucet as a Model Chaotic System
Crevier DW, Meister M. Synchronous period-doubling in flicker vision of salamander and man.
J Neurophysiol. 1998 Apr;79(4):1869-78.
Bing Jia, Huaguang Gu, Li Li, Xiaoyan Zhao. Dynamics of period-doubling bifurcation to chaos in the spontaneous neural firing patterns Cogn Neurodyn (2012) 6:89-106 DOI 10.1007/s11571-011-9184-7
A Garfinkel, ML Spano, WL Ditto, JN Weiss. Controlling cardiac chaos
Science 28 Aug 1992: Vol. 257, Issue 5074, pp. 1230-1235 DOI: 10.1126/science.1519060
R. M. May, D. M. G. Wishart, J. Bray and R. L. Smith Chaos and the Dynamics of Biological Populations
Source: Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 413, No. 1844, Dynamical Chaos (Sep. 8, 1987), pp. 27-44
Chialvo, D., Gilmour Jr, R. & Jalife, J. Low dimensional chaos in cardiac tissue. Nature 343, 653-657 (1990).
Xujun Ye, Kenshi Sakai. A new modified resource budget model for nonlinear dynamics in citrus production. Chaos, Solitons and Fractals 87 (2016) 51-60
Libchaber, A. & Laroche, C. & Fauve, Stephan. (1982). Period doubling cascade in mercury, a quantitative measurement. 43. 10.1051/jphyslet:01982004307021100.
Special thanks to Patreon Supporters:
Alfred Wallace, Arjun Chakroborty, Bryan Baker, DALE HORNE, Donal Botkin, halyoav, James Knight, Jasper Xin, Joar Wandborg, Lee Redden, Lyvann Ferrusca, Michael Krugman, Pindex, Ron Neal, Sam Lutfi, Tige Thorman, Vincent
Special thanks to:
Henry Reich for feedback on earlier versions of this video
Raquel Nuno for enduring many earlier iterations (including parts she filmed that were replaced)
Dianna Cowern for title suggestions and saying earlier versions weren't good
Heather Zinn Brooks for feedback on an earlier version.

Music from: "What We Discovered" "A Sound Foundation 1" "Seaweed" "Colored Spirals 4" "Busy World" "Children of Mystery"


  1. Rodrigo Aguilera

    Rodrigo Aguilera

    Prieš val

    hi, I had an idea, we can apply this method to the periodicity of PI, I remember that many mathematic are trying to find a patron, but if we can to model in 3D. (I’d like to think, numbers are tridimensional so we must view in this perspective the mathematic problem, I do not have the knowledge or the program to apply this but you do.

  2. Jesus Reynoso

    Jesus Reynoso

    Prieš 6 val

    Why if you have a bunch a gay rabbits?

  3. Man of Morbihan

    Man of Morbihan

    Prieš 7 val

    I don't understand what he is saying but it sounds very interesting....

  4. James Paddock

    James Paddock

    Prieš 15 val

    0:00 *eating rabbit stew on a fractal*

  5. Jeff M

    Jeff M

    Prieš dieną

    Universal constants are defined in the simulation parameters.

  6. Eric Newsom

    Eric Newsom

    Prieš dieną

    This explains mosquitoes on the Texas gulf coast.

  7. Cian Foley

    Cian Foley

    Prieš dieną

    Amazing videos.

  8. Multi Da

    Multi Da

    Prieš dieną

    Still want to return to monkey?

  9. Sharim Almaas

    Sharim Almaas

    Prieš dieną

    Can anyone please tell me which app he is using to plot those beautiful graphs??🥺😭

  10. iamdope


    Prieš dieną

    Which software he used to illustrate graph? Any idea?

  11. FractAlkemist


    Prieš dieną

    Interesting how it can "predict" population flux - can this also apply to Covid, the multiple "waves" we get??

  12. Johan Du Toit

    Johan Du Toit

    Prieš 2 dienas

    I need to get in contact with you. Got something pretty amazing to share. Thanks for this video!

  13. Iván


    Prieš 2 dienas

    Now my mind has fallen into a fascinating chaos

  14. Tom Russell

    Tom Russell

    Prieš 2 dienas

    kudos to you and your curiosity

  15. Nenad ИС XC Shuput

    Nenad ИС XC Shuput

    Prieš 2 dienas

    Not even this guy knows exactly what he is saying 🤣🤣

  16. charlie3k


    Prieš 2 dienas

    i watched this high and i feel like my mind entered a new dimension

  17. Fairyplay


    Prieš 2 dienas

    This video has become really relevant with covid lol (at least the R part at the beginning)

  18. Ray Skudlark

    Ray Skudlark

    Prieš 2 dienas

    I find it odd that ever since I can remember I have been trying to figure out this pattern 2 4 8 16 32 64 128 256 512 1024 as high as I could reach. And now to be learning all of this much later in life it really makes you wonder!? Thanks for the content man I have been watching and learning with you for I think what 8 or 9 years now and you have been a constant reminder I'm not the only one kicking these ideas around. I have been poor my whole life and never had a chance to apply my brain the way I wanted to. And being in low income areas it hard to have these kind of conversations with anyone. So thanks for doing this man really you and Micheal Vsauce I only hope the best to you guys.

  19. C Harris

    C Harris

    Prieš 3 dienas

    Finally the math that I already forgotten since high school looks interesting

  20. Mathew Jackson

    Mathew Jackson

    Prieš 3 dienas

    So I'm on the toilet, when you push more, more flow will come out but not all at once and evenly, then eventually your muscles can't take the stress and less flow will come out. Then your muscles recharge and you go at it again maybe harder or softer... Equation works in everything

  21. Omid Khoshravan Azar

    Omid Khoshravan Azar

    Prieš 3 dienas

    I don’t know why but this whole video felt like an unskippable ad

  22. Maulau Craw

    Maulau Craw

    Prieš 3 dienas

    Reverse this connection(selectablly applythe inverse function) and you have a fantastic modulus you can use to chart on an overlay the explicit proficiency to levels of implicit practicality of the teacher-student relevancy thereof.

  23. bumfartbumfart2


    Prieš 3 dienas

    i hope you have won some awards for your films

  24. The Zach

    The Zach

    Prieš 3 dienas

    I think this graph also represents the evolution of human intelligence. 👉Think about this: The same brain that created the theory of evolution had to first evolve itself.

  25. Mahir Balushi

    Mahir Balushi

    Prieš 3 dienas


  26. Daniel Edwards

    Daniel Edwards

    Prieš 3 dienas


  27. Brian Kleinschmidt

    Brian Kleinschmidt

    Prieš 3 dienas

    I love watching Mandelbrot renderings. That graphic just blew my mind. Beauty has a measure - math itself.

  28. Lion Deluxe

    Lion Deluxe

    Prieš 3 dienas

    This video made me obsessed. I didn’t sleep last night. This morning I went to my core editor and made a Mandelbrot’s Set visualizer and I watched this video for a second time. I now want to make a logistic map visualizer. Thank you Veritasium.

  29. mt2mgames


    Prieš 3 dienas

    this video is horrible. You keep conflating "the population" with "the percentage of the maximum possible population"

  30. Marre


    Prieš 3 dienas

    16:55 excited about chaos *HERESY* call the inquisiton

  31. Ruderaksha Karwa

    Ruderaksha Karwa

    Prieš 3 dienas

    Showerthought: every civilization follows the same pattern , I would say we crossed the curve somewhere between 70s-90s

  32. Drawing Masterclass

    Drawing Masterclass

    Prieš 4 dienas

    So much complexity and we still don't believe there is God.

  33. Shawn Bechard

    Shawn Bechard

    Prieš 4 dienas

    I keep hearing predictions that human populations will decline, but I don't think it is going to be anywhere near as soon as they think. We have been rising since the Black Plague supposedly.

  34. Nad G

    Nad G

    Prieš 4 dienas

    I LOVED this topic! It's insane! I knew that Mandelbrot set was pretty particular on its own but this! I want to know more

  35. Ish Kabibble

    Ish Kabibble

    Prieš 4 dienas

    This is amazing! I'm familiar with the Mandelbrot set from decades ago, but is that 3D z-axis section a new discovery?

  36. UhOhMeMeBiggestBoy


    Prieš 4 dienas

    Look at me just 16 and finding out about this instead of 32 welp anyway I have to go troubleshoot my brain

  37. Xandea Galleta

    Xandea Galleta

    Prieš 4 dienas

    I hurt myself in confusion. :(

  38. Dodd Rougeau

    Dodd Rougeau

    Prieš 4 dienas

    Spherical trigonometry will prove the Earth is flat. You haven't got the balls to research that truth.

  39. R Doody

    R Doody

    Prieš 4 dienas

    An application of math. Frustrating part of most math classes is the lack of application.

  40. Leandro Placencia

    Leandro Placencia

    Prieš 5 dienų

    19:39 10^10^100 Googolplex

  41. Leandro Placencia

    Leandro Placencia

    Prieš 5 dienų

    10^10^100 Googolplex

  42. Rotciv Inoccic

    Rotciv Inoccic

    Prieš 5 dienų

    BANG! .. My brain feels much better...

  43. Netemp Witemp

    Netemp Witemp

    Prieš 5 dienų

    It's the same about the human population. And it seems like we're at the peek right now and going down. That constant is like the pi of fractals

  44. deck monkey

    deck monkey

    Prieš 5 dienų

    School only teaches you the minimum you need to start the next grade. It doesn't teach you to think or be intelligent and never will. Look at how fast kids learn until they start school and then are held back from learning at the same pace by being forced to do it "the way I tell you".

  45. Jason Brunhard

    Jason Brunhard

    Prieš 5 dienų

    I want to thank you for your channel honestly. I rarely ever leave comments, but I am so IMPRESSED AND APPRECIATIVE for your work. You are bringing science out to the public forum so we, as a population, can engage in science. Science needs funding. It is what it is, and the content you provide is structured in a way for the general public can understand the unique and awe-inspiring physics that this universe has. FROM MY HEART THANK YOU FOR DOING YOUR BEST TO HELP THE HUMAN RACE EVOLVE.

  46. The Rodestarr

    The Rodestarr

    Prieš 5 dienų

    Holy hell. If they me a little about chaos theory in school I swear I would have been a mathematician by now.

  47. ich


    Prieš 5 dienų

    Which software did he use for plotting his graphs? 3:45

  48. Naz Fride

    Naz Fride

    Prieš 5 dienų

    Amazing. Thenks for the outstanding explanation of a pretty complex subject (for lay people)!

  49. Subhadeep Das

    Subhadeep Das

    Prieš 5 dienų

    If everyone will become vegetarian, there is no hunting or poaching and no disasters then we can find the date of extinction of a specific species 😯😯😯😯😯😯. This is mind blowing

    • oh no

      oh no

      Prieš 3 dienas

      this has nothing to do with vegetarians??

  50. Simranjeet Singh

    Simranjeet Singh

    Prieš 6 dienų

    Your calculation is wrong

  51. Ssenyonjo Jireh

    Ssenyonjo Jireh

    Prieš 6 dienų

    Can I still answer the question

  52. Ssenyonjo Jireh

    Ssenyonjo Jireh

    Prieš 6 dienų

    Can I still answer the question

  53. Chindulur Sai Kaushik

    Chindulur Sai Kaushik

    Prieš 6 dienų

    out of all the possibilities z-axis was the least expected

  54. Scripted Frames

    Scripted Frames

    Prieš 6 dienų

    we need "chaos" in schools, not the other chaos 😅

  55. Scripted Frames

    Scripted Frames

    Prieš 6 dienų


  56. Scripted Frames

    Scripted Frames

    Prieš 6 dienų

    This video proved me that I am a dumb

  57. Scripted Frames

    Scripted Frames

    Prieš 6 dienų

    This video proved me that I am a dumb, I didn't even understand a bit as a 11th grades student

  58. Leo Verran

    Leo Verran

    Prieš 6 dienų

    Rabbits times rabbits divided by coyotes plus hawks minus fox equals WTF are you talking about and who cares,...not even the rabbits care!

  59. Karan Jassal

    Karan Jassal

    Prieš 6 dienų

    This video was so enlightening! Thank you! I love how we can visually see the fractal from a simple equation, and this is exactly how I perceive the universe. "As above, so below"

  60. twobad


    Prieš 6 dienų

    hod up, someone has to tell me the graphing app that he used

  61. Miagi Fodder

    Miagi Fodder

    Prieš 6 dienų

    God man your 37 and only just found out about this. I'm 35 and just found out about it. Up your game dude

  62. Xing Yu

    Xing Yu

    Prieš 6 dienų

    this vid has saved my essay project 😂i've been learning how to determine period doubling in the last couple of months. But i had little clue that so many real life phenomena exhibits the bifurcation doubling behaviour. Impressed!

  63. FBI Agent

    FBI Agent

    Prieš 6 dienų

    I don’t get any of this but it sounds awesome

  64. Iron work Paul

    Iron work Paul

    Prieš 6 dienų

    The content is very good, a wonderful man with interesting knowledge

  65. Fuzzy Ankles

    Fuzzy Ankles

    Prieš 6 dienų

    holy shiet thats beautiful

  66. fffrikkie 123

    fffrikkie 123

    Prieš 7 dienų

    Life is a simulation confirmed

  67. Ishita Vyavahare

    Ishita Vyavahare

    Prieš 7 dienų

    what software is he using?

  68. Paolo Scaramuzzino

    Paolo Scaramuzzino

    Prieš 7 dienų

    how does it apply to the Covid-19 waves?

  69. O_0


    Prieš 7 dienų

    Wait, so you're telling me that you could set equations on google's calculator this whole time? Amazing

  70. Brian Kemery

    Brian Kemery

    Prieš 7 dienų

    I've heard a ton about the Mandelbrot set over the years...but when he rotated it into 3 dimensions and it matched with the bifurcation diagram, my brain literally melted.

  71. KG Guitar

    KG Guitar

    Prieš 7 dienų


  72. Anthony Tran

    Anthony Tran

    Prieš 7 dienų

    first 10 seconds and i went dumb

  73. Simon Lovelace

    Simon Lovelace

    Prieš 7 dienų

    When the firing of Neurons in your brain and rabbits and Mandelbrot and Phi and oh my God it's everywhere

  74. Juan David Barrada

    Juan David Barrada

    Prieš 7 dienų


  75. dolf1n1


    Prieš 7 dienų

    Wow I love the way you presented this topic so visually.

  76. Rocket Zing

    Rocket Zing

    Prieš 7 dienų

    Veritasium : video ratio movie producer : ''m i joke to you

  77. ash channan

    ash channan

    Prieš 8 dienų

    how many leaves on a tree ? - search - LTwindow Golden ratio Mrityunjaya Fibonacci Number Praveen Mohan - I like his explanation

  78. Milkymalk


    Prieš 8 dienų

    What if all these fundamental constants are such weird numbers (4.669, 3.1415..., and so on) because the computer universe.exe runs on uses something other than base 10?

  79. adib z

    adib z

    Prieš 8 dienų

    Everything is under control of God. Everything, under His calculation. Assalamualaikum

  80. XRay Plays

    XRay Plays

    Prieš 8 dienų


  81. Phillip Plyer

    Phillip Plyer

    Prieš 8 dienų

    I'm just now fi ding your videos and its creating chaos in my marriage! I feel a couple bifurcation coming on. Any sugar mommas out there wanna help me get to 4.6669!? 😜 But in all seriousness, your videos are awesome!

  82. steve


    Prieš 8 dienų

    I dont get it U just talk too much

  83. Phineas


    Prieš 8 dienų

    I struggled to understand this just like many people. But look up Feigenbaum Number on Numberphile, it'll make this easier to understand slightly

  84. John Worthington

    John Worthington

    Prieš 8 dienų

    I just like the math... You'll die tomorrow, but the rabbits will forever live until.. Reality..

  85. Mensa X

    Mensa X

    Prieš 8 dienų

    All we have to do now is track and follow every bunny rabbit to see if this is true

  86. rendzis


    Prieš 8 dienų

    In what day did god made this?😁

  87. mazhar chrome

    mazhar chrome

    Prieš 9 dienų

    Can you make a video about this equation with human population, where will be the equilibrium?

  88. unityelt


    Prieš 9 dienų

    It's like programming life

  89. Slow Motion

    Slow Motion

    Prieš 9 dienų

    OMG! I bet he was the most hated guy in school !

  90. Pula Vijaya

    Pula Vijaya

    Prieš 9 dienų

    Is world an illusion make a video sir

  91. Peacocks & Polar Bears

    Peacocks & Polar Bears

    Prieš 9 dienų

    This is insane. I've never seen something visualized like this.

  92. korteks visceralzen

    korteks visceralzen

    Prieš 9 dienų

    Thanks. I love this channel. No one explains this stuff.

  93. Betsy Larcom

    Betsy Larcom

    Prieš 9 dienų

    I was an ecology major in undergrad and everyone else thought we just went around hugging trees...

  94. Bare Bear Hands

    Bare Bear Hands

    Prieš 9 dienų

    Chaos is natural order.

  95. Eric Swenson

    Eric Swenson

    Prieš 9 dienų

    And no one thinks there is a creator that did all this by design? All these links and ratios no one can explain the existence of, and we think it all just came about by accident...

  96. Rohit Neemwal

    Rohit Neemwal

    Prieš 9 dienų

    so random numbers are not so random.

  97. Rohit Neemwal

    Rohit Neemwal

    Prieš 9 dienų

    universal constants are just some values given to simulator to simulate our universe.hece we are in simulator

  98. Rohit Neemwal

    Rohit Neemwal

    Prieš 9 dienų

    so , we are in simulation .

  99. Steven


    Prieš 9 dienų

    The mandelbrook fractal looks lika a turtle:)

  100. Vinyas Singh

    Vinyas Singh

    Prieš 10 dienų

    I guess the made up/unexplained answer of "42" we get to hear about has something to do with this universal constant of "4.669", I'm not sure though.